Creep and Shrinkage of Self-Compacting Concrete with … · Creep and Shrinkage of Self-Compacting Concrete with and without Fibers Farhad Aslani, Shami Nejadi Journal of Advanced

Creep and Shrinkage of Self-Compacting Concretewith and without FibersFarhad Aslani, Shami Nejadi

Journal of Advanced Concrete Technology, volume ( ), pp.11 2013 251-265

Recent Progress in Research on and Code Evaluation of Concrete Creep and Shrinkage in JapanTakumi Shimomura, Kenji SakataJournal of Advanced Concrete Technology, volume ( ), pp.2 2004 133-140

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Artificial Neural Network for Predicting Creep and Shrinkage of High Performance ConcreteJayakumar Karthikeyan, Akhil Upadhyay Navaratan.M Bhandari, ,Journal of Advanced Concrete Technology, volume ( ), pp.6 2008 135-142

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Journal of Advanced Concrete Technology Vol. 11, 251-265, October 2013 / Copyright © 2013 Japan Concrete Institute 251

Scientific paper

Creep and Shrinkage of Self-Compacting Concrete with and without Fibers Farhad Aslani1 and Shami Nejadi2

Received 28 November 2012, accepted 18 September 2013 doi:10.3151/jact.11.251

Abstract Fiber-reinforced self-compacting concrete (FRSCC) is a high-performance building material that combines positive aspects of fresh properties of self-compacting concrete (SCC) with improved characteristics of hardened concrete as a result of fiber addition. Considering these properties, the application ranges of both FRSCC and SCC can be covered. To produce SCC, either the constituent materials or the corresponding mix proportions may notably differ from the con-ventional concrete (CC). These modifications besides enhance the concrete fresh properties affect the hardened proper-ties of the concrete including creep and shrinkage. Therefore, it is vital to investigate whether all the assumed hypothe-ses about conventional concrete are also valid for SCC structures. In the present paper, a numerical and experimental study about creep and shrinkage behavior of FRSCC and SCC is performed. Two new creep and shrinkage prediction models based on the comprehensive analysis on the available models of both CC and SCC are proposed for FRSCC and SCC structures. In order to evaluate the predictability of the proposed models, an experimental program was carried out. For this purpose, four SCC mixes - plain SCC, steel, polypropylene, and hybrid FRSCC - are considered in the test pro-gram. Several specimens were loaded and deformation in non-loaded specimens was also measured to assess shrinkage. All specimens were kept under constant stress during at least 364 days in a climatic chamber with temperature and rela-tive humidity of 22ºC and 50%, respectively. Results showed that the new models were able to predict deformations with good accuracy, although providing deformations slight overestimated.

1. Introduction

Self-compacting concrete (SCC) can be placed and compacted under its own weight with little or no vibra-tion and without segregation or bleeding. SCC is used to facilitate and ensure proper filling and good structural performance of restricted areas and heavily reinforced structural members. It has gained significant importance in recent years because of its advantages. Recently, this concrete has gained wider use in many countries for different applications and structural configurations. SCC can also provide a better working environment by elimi-nating the vibration noise. Such concrete requires a high slump that can be achieved by superplasticizer addition to a concrete mix and special attention to the mix pro-portions. SCC often contains a large quantity of powder materials that are required to maintain sufficient yield value and viscosity of the fresh mix, thus reducing bleeding, segregation, and settlement. As the use of a large quantity of cement increases costs and results in higher temperatures, the use of mineral admixtures such as fly ash, blast furnace slag, or limestone filler could

increase the slump of the concrete mix without increas-ing its cost (Aslani and Nejadi 2012a, 2013).

Fiber-reinforced self-compacting concrete (FRSCC) is a relatively recent composite material that combines the benefits of the SCC technology with the advantages of the fiber addition to a brittle cementitious matrix. It is a ductile material that in its fresh state flows into the interior of the formwork, filling it in a natural manner, passing through the obstacles, and flowing and consoli-dating under the action of its own weight. FRSCC can mitigate two opposing weaknesses: poor workability in fiber-reinforced concrete (FRC) and cracking resistance in plain concrete. A few studies have been carried out on optimization of the mix proportion for the addition of steel or polypropylene fibers to SCC. Meanwhile, there is insufficient research on the mechanical properties of FRSCC. In mechanical terms, the greatest disadvantage of cementitious material is its vulnerability to cracking, which generally occurs at an early age in concrete struc-tures or members. Cracking may potentially reduce the lifetime of concrete structures and cause serious durabil-ity and serviceability problems (Aslani and Nejadi 2012b).

One critical property is creep of concrete. Creep de-pends on the characteristics of aggregate stiffness and texture, w/c ratio, volume of paste, volume of coarse aggregate, cement type, admixture type, curing method, ratio of volume to surface area, environmental condi-tions, magnitude of loads and age of loading. According to Neville (1996) mostly the hydrated cement paste ex-periences creep, while the aggregate is the only portion

1Centre for Built Infrastructure Research, School of Civil and Environmental Engineering, University of Technology Sydney, Australia. E-mail: [email protected] 2Centre for Built Infrastructure Research, School of Civil and Environmental Engineering, University of Technology Sydney, Australia.

F. Aslani and S. Nejadi / Journal of Advanced Concrete Technology Vol. 11, 251-265, 2013 252

which resists against creep. Therefore, creep is highly dependent on the stiffness of the chosen aggregate and its proportion within the mixture (Neville 1996). As a result, since creep mainly occurs in the cement paste, main concern arises that SCC may exhibit higher creep because of its high paste content.

Another essential mechanical parameter is the shrinkage of concrete. The overall shrinkage of concrete corresponds to a combination of several shrinkages, that is, plastic shrinkage, autogenous shrinkage, drying shrinkage, thermal shrinkage, and carbonation (chemi-cal) shrinkage. In designing of CC, shrinkage is fre-quently taken as drying shrinkage, which is the strain associated with the loss of moisture from the concrete under drying conditions, because with a relatively high water-to-cementitious material ratio (w/c) (higher than 0.40) CC exhibits a relatively low autogenous shrinkage <100×10-6 (Aslani and Nejadi 2011a). In contrast, the SCC used in the precast industry, namely for prestressed applications, has typically a low w/c ratio (0.32 to 0.40). These relatively low w/c ratios, coupled with a high content of binder lead to greater autogenous shrinkage. Such shrinkage increases and is notable in SCC because of the use of finely ground supplementary cementitious materials and fillers. Therefore, both drying and autoge-nous shrinkage deformations have to be accounted in the structural detailing of reinforced concrete and prestressed concrete members (Khayat and Long 2010).

Being aware that SCC usually has higher paste vol-ume and/or higher sand-to-aggregate ratio to achieve high workability, several researchers have claimed rela-tively large creep and shrinkage of SCC for pre-cast/prestressed concrete, resulting in larger prestress losse. In fact, although mechanical properties of SCC are superior to those of CC, creep and shrinkage of SCC are significantly high (Issa et al. 2005). Among others, Naito et al. (2006) also found that SCC exhibits higher shrinkage and creep than CC, which is due probably to the high fine aggregate and paste volume in the SCC.

On the other hand, Schindler et al. (2007) revealed that the shrinkage of SCC is similar or less than that of CC. When the shrinkage of SCC is compared to that of CC at 112 days, the sand-to-aggregate ratio effect is not significant for the shrinkage of SCC. The creep coeffi-cients of SCC mixtures were also smaller than those of CC at all loading ages. This was attributed to the low w/c.

The different methodology followed to obtain SCC in different countries and the limited number of studies concerning its long-term behavior make still not clear if current International Standards can be applied success-fully also for SCC. Moreover, it is not even assessed if long-term properties can be predicted with reference to conventional mechanical and physical parameters only (like strength or w/c) or the adoption of parameters con-cerning the mix design is needed.

2. Research significance

It is vital to investigate whether all the assumed hy-potheses used to design structures of conventional con-crete about creep and shrinkage are also valid for FRSCC and SCC structures. Thus, the objectives of this study are: (a) To review the accuracies of the CC creep and

shrinkage prediction models proposed by interna-tional codes of practice, including CEB-FIP (2010), ACI 209R (1997), Eurocode 2 (2004), JSCE (2002), AASHTO (2004; 2007) and AS 3600 (2009).

(b) To review the accuracies of the SCC creep and shrinkage prediction models proposed by Poppe and De Schutter (2005), Larson (2007), Cordoba (2007) and Khayat and Long (2010).

(c) To propose a new prediction creep and shrinkage model based on the comprehensive analysis of the available models and the experimental results da-tabase of both the CC and the FRSCC & SCC.

(d) To verify the predictability of the proposed models on experimental results conducted in a mix com-position previously used in the prefabrication of prestressed bridge girders, i.e. a FRSCC & SCC loaded at early ages.

3. Experimental program

An experimental program with shrinkage and creep tests was carried out in laboratory. For this purpose, four SCC mixes - plain SCC, steel, polypropylene, and hy-brid FRSCC - are considered in the test program. Sev-eral specimens were loaded and deformation in non-loaded specimens was also measured to assess shrink-age. All specimens were kept under constant stress dur-ing at least 364 days in a climatic chamber. 3.1 Materials 3.1.1 Cement In this experimental study, shrinkage limited cement (SLC) corresponding to the ASTM C183-08 (2000) (AS 3972, 2010) standard was used. SLC is manufactured from specially prepared portland cement clinker and gypsum. It may contain up to 5% of AS 3972 approved additions. The chemical, physical, and mechanical prop-erties of the cement used in the experiments are shown in Table 1. The chemical, physical, and mechanical properties adhere to the limiting value or permissible limits specified in AS 2350.2, 3, 4, 5, 8, and 11 (2006). 3.1.2 Fly ash It is important to increase the amount of paste in SCC because fly ash is an agent to carry the aggregates. Erar-ing fly ash (EFA) is a natural pozzolan. It is a fine cream/grey powder that is low in lime content. The chemical and physical properties of EFA used in the experimental study are given in Table 1. The chemical,


physical, and mechanical properties of the EFA used adhere to the limiting value or permissible limits speci-fied in ASTM C311-11b (2000) (ACI 232.2R-03, 2004; AS 2350.2, 2006; AS 3583.1, 2, 3, 5, 6, 12, and 13, 1998). 3.1.3 Ground granulated blast furnace slag Granulated blast furnace slag (GGBFS) is another sup-plementary cementitious material that is used in combi-nation with SLC. GGBFS used in the experiment origi-nated in Boral, Sydney, and it conformed to ASTM C989-06 (2000) (ACI 233R-95, 2000; AS 3582.2, 2001) specifications. The chemical and physical properties of GGBFS are given in Table 1. 3.1.4 Aggregate In this study, crushed volcanic rock (i.e., latite) coarse aggregate was used with a maximum aggregate size of 10 mm. Nepean river gravel with a maximum size of 5 mm and Kurnell natural river sand fine aggregates were also used. The sampling and testing of aggregates were carried out in accordance with ASTM C1077-13 (2000) (AS 1141, 2011; RTA 2006) and the results for coarse and fine aggregates are shown in Tables 2, respectively. 3.1.5 Admixtures The superplasticiser, viscosity-modifying admixture (VMA), and high-range water-reducing agent were used in this study. The new superplasticiser generation Gle-nium 27 complies with AS 1478.1 (2000) type High Range Water Reducer (HRWR) and ASTM C494 (2000) types A and F are used. The Rheomac VMA 362 viscos-ity modifying admixture that used in this study is a

ready-to-use, liquid admixture that is specially devel-oped for producing concrete with enhanced viscosity and controlled rheological properties. Pozzolith 80 was used as a high-range water-reducing agent in the mixes. It meets AS 1478 (2000) Type WRRe, requirements for admixtures. 3.1.6 Fibers In this study, two commercially available fibers, Dramix RC-80/60-BN type steel fibers and Synmix 65 type polypropylene (PP) fibers were used. The mechanical, elastic and surface structure properties of the steel and PP fibers are summarized in Table 3. 3.2 Mixture proportions One control SCC mixture (N-SCC) and three fiber-reinforced SCC mixtures were used in this study. Fiber-reinforced SCC mixtures contain steel (D-SCC), PP (S-SCC), and hybrid (steel + PP) (DS-SCC) fibers. The content proportions of these mixtures are given in Table 4. These contents were chosen to attempt to keep com-pressive strength to a level applicable to construction. As shown in Table 4, cement, fly ash, GGBFS, water, fine and coarse aggregates, VMA, and high range water reducing agent constituents amount are same for four mixes. But, fiber amount and superplasticiser that are used in the mixes are different.

A forced pan type of mixer with a maximum capacity of 150 liters was used. The volume of a batch with fi-bers was kept constant at 50 liters. First, powders and sand are mixed for 10 s and water and superplasticiser are added and mixed for 110 s and the coarse aggregate

Table 1 Properties of cement, fly ash, and ground granulated blast furnace slag (GGBFS). Cement Fly Ash GGBFS

Chemical properties Chemical properties Chemical properties CaO 64.5 % Al2O3 26.40 % Al2O3 14.30 % SiO2 19.3 % CaO 2.40 % Fe2O3 1.20 % Al2O3 5.2 % Fe2O3 3.20 % MgO 5.40 % Fe2O3 2.9 % K2O 1.55 % Mn2O3 1.50 % MgO 1.1 % MgO 0.60 % SO3 0.20 % SO3 2.9 % Mn2O3 <0.1 % Cl 0.01 % K2O 0.56 % Na2O 0.47 % Insoluble Residue 0.50 % Na2O <0.01 % P2O5 0.20 % LOI -1.10 %

Cl 0.02 % SiO2 61.40 % Physical properties LOI 2.8 % SO3 0.20 % Fineness Index 435 m2/kg Physical properties SrO <0.1 %

Autoclave Expansion TiO2 TiO2 1.00 % Fineness Index 405 m2/kg Physical properties

Mechanical properties Moisture <0.1 % Initial Setting Time 90 mins Fineness 45 micron 78% passed Final Setting Time 135 mins Loss on Ignition 2.30 %

Soundness 1.0 mm Sulfuric Anhydride 0.20 % Drying Shrinkage 590 μstrain Alkali Content 0.50 %

f'c (3 Days) 37.2 MPa Chloride Ion <0.001 % f'c (7 Days) 47.3 MPa Relative Density 2.02 %

f'c (28 Days) 60.8 MPa Relative Water Requirement 97 %

Relative Strength 28 Days 88 %


is added and at the end fibers are added to the pan and mixed for 90 s.

3.3 Samples’ preparation and curing conditions We used three φ100 mm × 200 mm molds for the de-termination of compressive strength at age 28 days and three cylindrical molds φ100 mm × 200 mm are used for the determination of the modulus of elasticity. Speci-mens for testing the hardened properties are prepared by direct pouring of concrete into molds without compac-tion. The specimens are kept covered in a controlled chamber at 20 ± 2℃ for 24 h until demolding. Thereaf-

ter, the specimens are placed in water presaturated with lime at 20℃. These specimens are tested at. For each test, separated specimens are used and surface of speci-mens are smoothed.

Three 75 mm × 75 mm × 280 mm molds are used for the determination of drying shrinkage. After demolding shrinkage specimens, all of them are stored in standard temperate moist curing conditions at the measuring laboratory for a minimum of 24 h prior to initial meas-urement. Five φ100 mm × 200 mm cylinders are used for the determination of creep in one creep rig. The ap-plied stress value was determined by the 40% of the 28

Table 2 Properties of crushed latite volcanic rock coarse aggregate, Nepean river gravel fine aggregate, and Kurnell natural river sand fine aggregate.

Crushed latite volcanic rock coarse aggregate

Nepean river gravel fine aggregate Kurnell natural river sand fine aggregate

Characteristics Results Characteristics Results Characteristics Results

Sieve size Passing (%) Sieve size Passing

(%) Sieve size Passing (%)

13.2 mm 100 6.7 mm 100 1.18 mm 100 9.5 mm 89 4.75 mm 99 600 micron 98 6.7 mm 40 2.36 mm 83 425 micron 87

4.75 mm 7 1.18 mm 64 300 micron 46 2.36 mm 1 600 micron 42 150 micron 1

1.18 mm 1 425 micron 28 Material finer than

75 micron in aggregate by washing (%)

Nil

Material finer than 75 micron (%) 1 300 micron 19 Uncompacted Bulk

Density (t/m3) 1.39

Mis-shapen particles (%) 150 micron 8 Compacted Bulk Density (t/m3) 1.54

Ratio 2:1 13 Material finer than 75 micron (%) 3 Particle Density

(Dry) (t/m3) 2.58

Ratio 3:1 1 Uncompacted Bulk Density (t/m3) 1.52 Particle Density

(SSD) (t/m3) 2.59

Flakiness Index (%) 20 Compacted Bulk Density (t/m3) 1.64 Apparent Particle

Density (t/m3) 2.62

Uncompacted Bulk Density (t/m3) 1.36 Particle Density (Dry) (t/m3) 2.58 Water Absorption (%) 0.6

Compacted Bulk Density t/m3 1.54 Particle Density (SSD) (t/m3) 2.60 Silt Content (%) 4 Moisture condition of

the aggregate (%) 1.3 Apparent Particle Density (t/m3) 2.63

Particle Density (Dry) (t/m3) 2.65 Water Absorption (%) 0.7 Particle Density (SSD) (t/m3) 2.70 Silt Content (%) 7

Apparent Particle Density (t/m3) 2.79

Degradation Factor of Fine Aggregate

The wash water after using permitted 500ml was: CLEAR

90

Water Absorption (%) 1.9 Moisture Content (%) 5.5

Ave. Dry Strength (kN) 391 Method of Determining Voids Content

Ave. Wet Strength (kN) 293 % Voids 41.7 Wet/Dry Strength

Variation (%) 25 The mean Flow Time (Sec.) 26.5

Test fraction (mm) -9.5+6.7 The amount of significant

breakdown (%) The size of testing cylinder =

150 mm diam.

<0.2

Los Angeles Value Grd. 'K' (%Loss) 13


days compressive strength results. All shrinkage and creep specimens are hold in the drying room with suita-bly controlled temperature, humidity and air circulation. The temperature and relative humidity of the drying room was 23±2ºC and 50±5% respectively.

3.4 Samples’ test methods The compressive strength test, performed on φ100 mm × 200 mm cylinders, followed AS 1012.14 (1991) and ASTM C39 (2000) tests for compressive strength of cylindrical concrete specimens. The cylinders were loaded in a testing machine under load control at the rate of 0.3 MPa/s until failure. The modulus of elasticity test that followed the AS 1012.17 (1997) and ASTM C469 was done to φ100 mm × 200 mm cylinders.

The shrinkage test, performed on 75 mm × 75 mm × 280 mm prisms, followed AS 1012.13 (1992) determi-nation of the drying shrinkage of concrete test method. The creep test is performed on five φ100 mm × 200 mm cylinders in one creep rig, followed AS 1012.16 (1996) determination of creep of concrete cylinders in com-pression test method.

3.5 Properties of fresh concrete The experiments required for the SCC are generally carried out worldwide under laboratory conditions. These experiments test the liquidity, segregation, placement, and compacting of fresh concrete. Conven-tional workability experiments are not sufficient for the evaluation of SCC. Some of the experiment methods developed to measure the liquidity, segregation, place-

ment, and compaction of SCC are defined in the Euro-pean guidelines (2005) and ACI 237R-07 (2007) for SCC, including specification, production and use as slump–flow, V-funnel, U-box, L-box and fill-box tests.

This study performed slump flow, T50cm time, J-ring flow, V-funnel flow time, and L-box blocking ratio tests. In order to reduce the effect of loss of workability on the variability of test results, the fresh properties of the mixes were determined within 30 min after mixing. The order of testing is as follows: 1. Slump flow test and measurement of T50cm time; 2. J-ring flow test, meas-urement of difference in height of concrete inside and outside the J-ring and measurement of T50cm time; 3. V-funnel flow tests at 10 s T10s and 5 min T5min; and 4. L-box test.

4. Experimental results

4.1 Properties of fresh concrete The results of various fresh properties tested by the slump flow test (slump flow diameter and T50cm); J-ring test (flow diameter); L-box test (time taken to reach 400 mm distance T400mm, time taken to reach 600 mm dis-tance T600mm, time taken to reach 800 mm distance TL, and ratio of heights at the two edges of L-box [H2/H1]); V-funnel test (time taken by concrete to flow through V-funnel after 10 s T10s); the amount of entrapped air; and the specific gravity of mixes are given in Table 5. The slump flow test judges the capability of concrete to de-form under its own weight against the friction of the surface with no restraint present. A slump flow value

Table 3 The physical and mechanical properties of fibers.

Fibre type Fibre name Density (kg/m3)

Length (l)

Diameter (d)

Aspect ratio (l/d)

Tensile strength (MPa)

Modulus of elasticity

(GPa)

Cross-section form

Surface structure

Steel Dramix RC-80/60-BN 7850 60 0.75 80.0 1050 200 Circular Hooked end

Polipropylene (PP) Synmix 65 905 65 0.85 76.5 250 3 Square Rough

Table 4 The proportions of the concrete mixtures (based on SSD condition).

Constituents N-SCC D-SCC S-SCC DS-SCC Cement (kg/m3) 160 160 160 160 Fly Ash (kg/m3) 130 130 130 130 GGBFS (kg/m3) 110 110 110 110 Cementitious content (kg/m3) 400 400 400 400 Water (lit/m3) 208 208 208 208 Water cementitious Ratio 0.52 0.52 0.52 0.52 Fine aggregate (kg/m3) Coarse Sand 660 660 660 660 Fine Sand 221 221 221 221 Coarse aggregate (kg/m3) 820 820 820 820 Admixtures (lit/m3) Superplasticiser 4 4.86 4.73 4.5 VMA 1.3 1.3 1.3 1.3 High range water reducing agent 1.6 1.6 1.6 1.6 Fibre content (kg/m3) Steel - 30 - 15 PP - - 5 3


ranging from 500 to 700 mm for self-compacting con-crete was suggested (European guidelines, 2005). At a slump flow > 700 mm the concrete might segregate, and at <500 mm, the concrete might have insufficient flow to pass through highly congested reinforcements. All the mixes in the present study conform to the above range, because the slump flow of SCC is in the range of 600–700 mm. The slump flow time for the concrete to reach a diameter of 500 mm for all mixes was less than 4.5 s. The J-ring diameters were in the range of 560–655 mm. In addition to the slump flow test, a V-funnel test was also performed to assess the flowability and stability of SCC. V-funnel flow time is the elapsed time in seconds between the opening of the bottom outlet, depending when it is opened (T10s and T5min), and the time when light becomes visible at the bottom when observed from the top. According to the European guidelines (2005), a period ranging from 6 to 12 s is considered adequate for SCC. The V-funnel flow times in the experiment were in the range of 7–11 s. The test results of this investigation indicated that all mixes met the requirements of allow-able flow time. About V-funnel flow time test results for the N-SCC mix was 6 s and for the D-SCC was 7 s and for other fiber reinforced SCC mixes are blocked, obvi-ously.

The maximum size of coarse aggregate was restricted to 10 mm to avoid a blocking effect in the L-box for N-SCC mix. The gap between rebars in the L-box test was 35 mm. The L-box ratio H2/H1 for the N-SCC mix was above 0.8 which is, according to the European guide-lines and, obviously, for other mixes is blocked. A total spread over 700 mm was measured and no sign of seg-regation or considerable bleeding in any of the mixtures was detected as the mixtures showed good homogeneity and cohesion.

4.2 Compressive strength and modulus of elas-ticity Table 6 presents the average compressive strength and modulus of elasticity of N-SCC, D-SCC, S-SCC, and

DS-SCC mixes. 4.3 Deformation measurements results Results of the shrinkage strain, creep strain, and total strain for all sets of loaded specimens are presented in Figs. 1-3 and Table 7. After the commencement of dry-ing, the shrinkage strain developed rapidly within the first two or three months and more than 50% of shrink-age occurred during this period. The maximum meas-ured final shrinkage strain or N-SCC, D-SCC, S-SCC, and DS-SCC, and N-CC mixtures were 870, 844, 823, and 882 microstrains after 364 days. The maximum measured final shrinkage strain for SCC mixtures are not much different from each other.

The creep strains increased quickly for the first few weeks after loading, with almost 50% of creep occur-ring in the first 40 days after loading. The final creep strains for N-SCC, D-SCC, S-SCC, DS-SCC, and N-CC mixtures were 1773, 1686, 1997, and 1736 microstrains after 364 days. There are very interesting results here the creep coefficient of DS-SCC mixture has same trend like N-CC. But, the other SCC mixtures have different behavior. The maximum creep coefficient is related to S-SCC with PP fibers in the mixture. The creep coeffi-cient of S-SCC mixture at age 364 days is 11%, 15%, and 13% higher than N-SCC, D-SCC, and DS-SCC mixtures, respectively.

5. Numerical analysis

Based on the recent studies of Aslani and Nejadi (2011 a,b) following procedure are used for comparing avail-able conventional concrete creep and shrinkage models: 1. Establish an experimental database for creep and shrinkage results. 2. Establish creep and shrinkage available prediction models database. 3. Comparing creep and shrinkage models with SCC experimental results database. 4. Proposing SCC creep and shrinkage models based on the pervious comparisons. 5. Verifica-tion of proposed SCC creep and shrinkage models with

Table 5 The SCC mixes workability characteristics. Workability characteristics N-SCC D-SCC S-SCC DS-SCC Average spreading diameter (mm) 680 670 700 650 Flow time T50cm (s) 2.7 3.8 2.5 3.2 Average J-Ring diameter (mm) 655 580 570 560 Flow time T50cm J-Ring (s) 3.2 5 6 5 L-box test 0.87 Blocked* Blocked Blocked Flow time V-funnel (s) 6 7 Blocked Blocked V-funnel at T5minutes (s) 4 5 Blocked Blocked Entrapped air (%) 1.3 1.2 1.2 1.0 Specific gravity (kg/m3) 2340 2274 2330 2385 * Fibers are the main reason for blockage.

Table 6 The experimental result of compressive strength and modulus of elasticity of SCC mixes.

N-SCC D-SCC S-SCC DS-SCC Compressive strength (MPa) 33.60 38.30 33.00 42.00 Modulus of Elasticity (MPa) 3599 3870 3424 3771


experimental results tests that have been done in this study. 5.1 Creep and shrinkage experimental results database Tables 8-9 present a general summary of the creep and shrinkage concrete mixtures included in the database. The database comprises test results from 11 different investigations, with a total of 52 SCC and 11 CC mix-tures for creep tests. Also, the database comprises test

results from 14 different investigations, with a total of 165 different SCC mixtures and 21 CC mixtures for shrinkage tests. Tables 8-9 also include complimentary information regarding the applied stress to the creep specimens, age of concrete when shrinkage begins (days), final age of the concrete, relative humidity (RH), type of the specimen, type of the cement and filler. 5.2 Creep and shrinkage models This paper also, assesses the accuracy of seven com-monly used international code type models that are used to predict creep and shrinkage strains. These empirically based models, which vary widely in their techniques, require certain intrinsic and/or extrinsic variables, such as mix proportions, material properties and age of load-ing as input. The models considered are listed in Table 10, which also shows the factors accounted by each model. In this study the accuracy of the creep and shrinkage prediction models proposed by international codes of practice, including: CEB-FIP (2010), ACI 209R (1997), Eurocode 2 (2004), JSCE (2002), AASHTO (2004), AASHTO (2007) and AS 3600 (2009) are compared with the actual measured creep and shrinkage strains.

As shown in the Table 11, the AASHTO (2007), JSCE (2002), Eurocode 2 (2004) and AASHTO (2004) models provided better prediction of creep data for CC mixture in the experimental database with a coefficient of correlation factor (R2) of 0.90, 0.89,0.89 and 0.86 compared to other models. Also, as shown in the Table 11, for SCC mixture in the experimental database, AASHTO (2004), JSCE (2002) and ACI 209R (1992) models provided better prediction of creep data with a coefficient of correlation factor (R2) of 0.87, 0.87 and 0.84 compared to other models.

AASHTO (2004), JSCE (2002) and ACI 209R (1992) CC creep models that have conservative predictions for SCC mixtures in the database are different in the certain intrinsic and/or extrinsic variables. As mentioned in the Table 11, the AASHTO (2004) creep model has not any intrinsic factors but the JSCE (2002) and ACI 209R (1992) creep models have a good consideration of both intrinsic variables (i.e. aggregate type, aggre-gates/cement ratio, air content, cement content, cement type, concrete density, fine/total aggregate ratio, slump, w/c ratio, and water content) and extrinsic variables (i.e. age at the first loading, age of sample, applied stress, characteristic strength at loading, cross-section shape, curing conditions, compressive strength at 28 days, du-ration of load, effective thickness, elastic modulus at age of loading, elastic modulus at 28 days, relative hu-midity, temperature, and time drying commences). The modified composition of SCC in comparison with CC influences the creep behavior of the concrete. Therefore, it is important to include some important variables that have impact on this behavior. By consideration these variables, JSCE (2002) creep model have good intrinsic and extrinsic variables.

Fig. 1 Creep strain for all specimens loaded.

Fig. 2 Shrinkage strain for all specimens.

Fig. 3 Total strain for all specimens loaded.


As show in the Table 12, for CC mixture in the ex-perimental database, the AASHTO (2007) and JSCE (2002) models provided a better prediction of drying shrinkage data with a coefficient of correlation factor (R2) of 0.88 and 0.84 compared to other models. Also, as shown in the Table 12, the AASHTO (2007), JSCE (2002) and AS 3600 (2009) models provided a better prediction of SCC mixture in the experimental database drying shrinkage data with a coefficient of correlation factor (R2) of 0.86, 0.83 and 0.80 compared to com-pared to other models.

The CC shrinkage models of AASHTO (2007) and JSCE (2002) that have conservative predictions for SCC mixtures in the database are different in the certain in-trinsic and/or extrinsic variables. As mentioned in the Table 10, the AASHTO (2007) shrinkage model has not any intrinsic factors but the JSCE (2002) shrinkage model has a good consideration of both intrinsic and extrinsic variables. When compared to the CC, the modified composition of SCC has influence in the shrinkage behavior of concrete. Therefore, it is impor-tant to involve some important variables that have im-pact on this behavior. By consideration these variables, JSCE (2002) shrinkage model have good intrinsic and extrinsic variables.

5.3 Proposed creep model The comparison of the different models and the experi-mental database shows that ACI 209R (1997), JSCE (2002) and AASHTO (2004) models have conservative creep coefficient predictions. In this study, based on

required certain intrinsic and/or extrinsic variables for SCC, JSCE (2002) creep model gives the good ap-proximation of the creep coefficient. Therefore, with the JSCE (2002) creep model as a basis, it is tried to formu-late some suggestions to include the c/p (cement-to-powder) ratio into the formulas in order to obtain a bet-ter prediction of the time-dependent deformations of normal strength and high strength of SCC. These results are showed into Eq. (1) to Eq. (10). A) For the normal strength SCC with range of appli-

cability (see the denomination of the parameters in the Notation Section):

45% 80%RH≤ ≤ ; 3 3120 / 230 /kg m w kg m≤ ≤ ; 100 / 300mm v s mm≤ ≤ ; 0.30 / 0.65w c≤ ≤ ;

,28 55c df MPa≤ ; 3 3260 / 500 /kg m c kg m≤ ≤ .

{ }0.54

1

( , , ) 1 exp 0.09( )(0.015 1.35( / )) / 0.65cc 0 cp crt t t t t

c p for c pε σ ε

−

⎡ ⎤′ ′ ′ ′ ′= × − − −⎣ ⎦× + <

(1)

{ }0.54

1

( , , ) 1 exp 0.09( )(0.015 1.05( / )) / 0.65cc 0 cp crt t t t t

c p for c pε σ ε

−

⎡ ⎤′ ′ ′ ′ ′= × − − −⎣ ⎦× + <

(2)

0. ( , )1cp

t t αμ λ σσ

κ+

′ =−

non-linear creep amplification function (3) where μ and λ and α are additional parameters to be ob-tained from a least square minimization procedure start-ing from experimental data μ=0.90, λ=1.80, α=2.10; moreover, the stress function σ(t, t0) is the actual stress/strength ratio, being:

Table 7 The experimental result of shrinkage and creep strains of SCC mixes. N-SCC D-SCC S-SCC DS-SCC Time shrinkage (μm) creep (μm) shrinkage (μm) creep (μm) shrinkage (μm) creep (μm) shrinkage (μm) creep (μm)

0hr 0 0 0 0 0 0 0 0 2hr 0 311 3 117 11 104 10 116 6hr 1 393 8 182 17 202 10 148 1d 12 479 22 309 42 389 36 220 2d * * 42 412 79 459 64 316 3d 52 601 81 515 105 518 95 385 4d 64 672 98 571 134 569 * * 5d 91 742 * * * * 142 545 6d 121 827 119 654 166 671 172 610 7d 150 872 150 680 204 730 210 670

14d 242 991 251 835 339 1024 310 819 21d 329 1105 348 974 419 1116 394 951 28d 403 1172 404 1035 479 1202 436 1060 56d 567 1344 565 1222 631 1432 596 1226 84d 693 1469 650 1305 713 1595 688 1341

112d 756 1525 709 1368 757 1671 758 1414 140d 793 1570 749 1428 803 1718 830 1469 168d 827 1603 780 1493 816 1759 849 1530 196d 848 1647 811 1538 830 1815 869 1569 224d 870 1696 823 1581 844 1858 882 1612 252d 896 1720 833 1617 853 1894 898 1646 280d 916 1734 847 1636 861 1927 907 1676 308d 930 1753 853 1656 866 1960 917 1704 336d 947 1765 860 1676 869 1984 921 1728 364d 957 1773 868 1686 874 1997 925 1736


Table 8 Creep experimental results database.

Reference No. of SCC

mixtures

No. of CC

mixtures

Applied stress to the creep specimens

Final age of concrete

(days) R.H. (%) Type of specimen (mm) Type of

cement Type of Filler

Chopin et al. (2003) 5 1

40% or 60% of the compressive strength

at 28 days 365 50 Cylinder (90 × 280) CEM I Limestone

Poppe and De Schutter

(2005) 6 0 1/3 of the compressive

strength at 28 days 1400 60 Prism (150×150×500) CEM I 42.5 R, CEM I 52.5 Limestone

Horta (2005) 6 0 40% of the compressive strength at 28 days 70, 200 50 Cylinder (150 × 300) CEM I ,

CEM III Fly ash and

GGBFS

Larson (2006) 1 0 40% of the compressive strength at 28 days 520 50

Prism (101.6×101.6×609.6)

and Cylinder (114.3×609.6)

CEM III Limestone

Turcry et al. (2006) 3 3 20% of the compressive

strength at 7 days 65, 100 50 Cylinder (110 x 200) CEM I 52.5, CEM II 42.5 Limestone

Cordoba (2007) 4 1 30% of the compressive

strength at 28 days 365 50 Cylinder (101.6 × 203.2), (101.6 × 1057.8) CEM I/II Fly ash and

GGBFS

Heirman et al. (2008) 7 1 ±1/3 of the compressive

strength at 28 days 70 60 Cylinder (120 × 300) CEM I 42.5 R,

CEM III/A 42.5 N LA

Limestone

Oliva and Cramer (2008) 11 4 40% of the compressive

strength at 28 days 495 50 Cylinder (152.4 × 213.6) CEM I GGBFS

Kim (2008) 4 4 Changeable for each mixture 150 50 Cylinder (100×200) CEM III Fly ash and

Limestone Zheng et al.

(2009) 7 1 30% of the compressive strength at loading days 150 60 Prism (100×100×400) CEM I Fly ash

Loser and Leemann

(2009) 1 1 Changeable for

each mixture 91 70 Prism (120×120×360) CEM I 42.5 N, CEM II/A-LL

45.2 N

Fly ash and Limestone

Total of 71 mixtures 55 16

Table 9 Shrinkage experimental results database.

Reference No. of SCC

mixtures

No. of CC

mixtures

Age of concrete

when shrinkage

begins (days)

Final age of concrete (days)

R.H. (%) Type of specimen (mm) Type of cement Type of filler

Chopin et al. (2003) 5 1 1 365 50 Cylinder (90 × 280) CEM I Limestone

Poppe and De Schutter (2005) 4 0 1 1400 60 Prism (150×150×500) CEM I 42, 5 R, CEM I

52,5 Limestone

Horta (2005) 6 0 1 200 50 Cylinder (150 × 300) CEM I , CEM III Fly ash and GGBFS

Larson (2006) 1 0 1 520 50 Prism (101.6×101.6×609.6) and Cylinder (114.3×609.6) CEM III Limestone

Turcry et al. (2006) 3 3 1 120, 150,

210 50 Prism (70×70×280) CEM I 52.5, CEM II 42.5 Limestone

Cordoba (2007) 4 1 1 365 50 Cylinder (101.6 × 203.2), (101.6 × 1057.8) CEM I/II Fly ash and GGBFS

Heirman et al. (2008) 7 1 1 98 60 Cylinder (120 x 300) CEM I 42.5 R, CEM

III/A 42.5 N LA Limestone

Bhattacharya (2008) 6 2 1 90 50 Prism (76.2×76.2×311.2) CEM I Limestone, Silica

fume and Slag Oliva and Cramer

(2008) 11 4 1 350, 495 50 Prism (101.6×101.6×285.75) CEM I GGBFS

Hwang and Kha-yat (2009) 10 2 1 56 50 Prism (75x75×285)

CSA type Gub-F/SF, Gub-S/SF and quaternary

blended cement

Fly ash and Lime-stone

Ma et al. (2009) 16 0 1 120, 150 60 Prism (100×100×515) CEM I Fly ash Loser and Lee-mann (2009) 13 3 1 91 70 Prism (120×120×360) CEM I 42.5 N, CEM

II/A-LL 45.2 N Fly ash and Silica

fume

Güneyisi et al. (2010) 63 2 1 50 50 Prism (70×70×280) CEM I

Fly ash, GGBFS, Silica fume and

Metakaolin

Khayat and Long (2010) 16 2 1 300 50 Cylinder (150×300)

MS and HE (similar to ASTM C150 Type I/II

and Type III) Fly ash

Total of 186 mixtures 165 21


00

( )( , )

( )cm

tt t

f tσ

σ = (4)

in the case of constant applied load. In Eq. (3), numera-tor and denominator indicate the effect of sustained load and the effect of a damage level due to instantaneous loading. The law fcm(t) representing the evolution with time of compression strength has been defined by modi-fying MC90 proposal according to expression:

,2828( ) .exp 1

n

cm cf t f st

⎡ ⎤⎛ ⎞⎛ ⎞′ ′= −⎢ ⎥⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎢ ⎥⎝ ⎠⎣ ⎦ (5)

where parameters s' and n have been specifically cali-brated for each SCC concrete mix by using experimen-tal results previously described. According to the avail-able data, parameters s' and n range from 0.2–0.6, and 0.28–0.35, respectively. The adoption of function σ(t, t0) allows for variable rate of increase of mechanical prop-erties be taken into account, particularly important for concretes loaded at early ages. Finally, the non-linear behavior during the load application has been intro-duced in Eq. (3) according to the conventional scalar damage index κ = 1 − E/E0, where E is the secant stiff-ness at the end of loading and E0 is the initial tangent stiffness. Usually damage index κ is about 0.10–0.15 or 0.22–0.35 for low (0.35fcm(t)) or medium (0.55fcm(t)) applied stress levels, respectively.

cr bc dcε ε ε′ ′ ′= + (6)

{ } 0.672.0 2.4 1017.5( ) ( / ) ln( ) 10bc c w w c tε − −⎡ ⎤′ ′= + ×⎣ ⎦ (7)

4.2 1.4

2.2 0.36 100.30

0

4500( / ) ( )10/ln 1

10 100dc

w c c wv s RH t

ε − −−

⎡ ⎤+⎢ ⎥′ = ×⎡ ⎤⎛ ⎞ ⎧ ⎫⎢ ⎥−⎨ ⎬⎜ ⎟⎢ ⎥⎢ ⎥⎝ ⎠ ⎩ ⎭⎣ ⎦⎣ ⎦

(8)

B) For the high strength SCC with range of applica-bility by using Eq. (3-5):

45% 90%RH≤ ≤ ; 3 3120 / 230 /kg m w kg m≤ ≤ ; 100 / 300mm v s mm≤ ≤ ; 0.30 / 0.65w c≤ ≤ ;

,2855 100c df MPa≤ ≤ ; 3 3260 / 500 /kg m c kg m≤ ≤ .

0.678

4 (1 /100) 350( , , ) ln( 1)

12 ( )(10 ( / ) ) / 0.65

cc cp

c

0w RH

t t t t tf t

c p for c p

ε σ− +

′ ′ ′ ′= × − +′ ′+

× × <

⎡ ⎤⎢ ⎥⎣ ⎦ (9)

0.701

4 (1 /100) 350( , , ) ln( 1)

12 ( )(13 ( / ) ) / 0.65

cc cp

c

0w RH

t t t t tf t

c p for c p

ε σ− +

′ ′ ′ ′= × − +′ ′+

× × <

⎡ ⎤⎢ ⎥⎣ ⎦ (10)

where for t0, t' and t is replaced by:

( )1 0

4000exp 13.65

273 /

n

ii i

t tT t T

ΔΔ=

= −+

⎡ ⎤⎢ ⎥⎣ ⎦

∑

Table 10 Summary of factors accounted for by different prediction models.

Models

CEB

-FIP

(201

0)

AC

I 209

R (1

997)

Euro

code

2

(200

4)

JSC

E (2

002)

AA

SHTO

(200

4)

AA

SHTO

(200

7)

AS

3600

(200

9)

Aggregate Type A/C Ratio

Air Content ■ ■Cement Content ■ ■ ■

Cement Type Concrete Density ■ ■

Fine/Total Aggregate Ratio (Mass) ■ ■

Slump ■ ■w/c Ratio ■

Intri

nsic

Fac

tors

Water Content ■ Age at First Loading ■ ■ ■ ■ ■ ■ ■

Age of Sample ■ Applied Stress ■ ■ ■ ■ ■Characteristic

Strength at Loading

Cross-section Shape ■ Curing Conditions

Compressive Strength at 28 Days ■ ■ ■ ■ ■ ■ ■

Duration of Load ■ ■ ■ ■ ■Effective Thickness ■ ■ ■ ■ ■ ■ ■Elastic Modulus at

Age of Loading

Elastic Modulus at28 Days ■ ■ ■ ■ ■

Relative Humidity ■ ■ ■ ■ ■ ■ ■Temperature ■

Extri

nsic

Fac

tors

Time Drying Commences

Table 11 Coefficient of correlation factor (R2) of creep prediction models for CC and SCC.

CC SCC Creep prediction models

R2 R2 CEB-FIP (2010) 0.41 0.58 ACI 209R (1997) 0.79 0.84 Eurocode 2 (2004) 0.89 0.80

JSCE (2002) 0.89 0.87 AASHTO (2004) 0.86 0.87 AASHTO (2007) 0.90 0.80

Table 12 Coefficient of correlation factor (R2) of shrinkage prediction models for CC and SCC.

CC SCC Shrinkage prediction models R2 R2

CEB-FIP (2010) 0.70 0.57 ACI 209R (1997) 0.62 0.66 Eurocode 2 (2004) 0.72 0.55

JSCE (2002) 0.84 0.83 AASHTO (2004) 0.42 0.47 AASHTO (2007) 0.88 0.86 AS 3600 (2009) 0.65 0.80


5.4 Proposed shrinkage model The comparison of the different models and the experi-mental database shows that ACI 209R (1997), JSCE (2002) and AASHTO (2004) models have conservative drying shrinkage predictions. In this study, based on required certain intrinsic and/or extrinsic variables for SCC, JSCE (2002) drying shrinkage model gives the best approximation of the drying shrinkage strain. Therefore, with the JSCE (2002) model as a basis, it is tried to formulate some suggestions to include the ce-ment-to-powder (c/p) ratio into the formulas in order to obtain a better prediction of the time-dependent defor-mations of normal strength and high strength of SCC. These results are showed into Eq. (11) to Eq. (23).

For the normal strength SCC (with range of applica-bility same as creep proposed model):

( ) ( ){ }( 2.4( / ) 2.3)0 0, 1 exp 0.1 c p

cr sht t t tε ε − +′ ′= − − −⎡ ⎤⎣ ⎦ (11)

{ }( )5

2

50 78 1 exp 38.3 ln100

10/

0.92 ln 5 ln10

sh

RHw

w v s

c

for c/p 0.65

ε −

− + − +

′ = ×

− −

≥

⎡ ⎛ ⎞ ⎤⎜ ⎟⎢ ⎥⎝ ⎠

⎢ ⎥⎢ ⎥⎛ ⎞ ⎡ ⎛ ⎞⎤

⎜ ⎟ ⎜ ⎟⎢ ⎥⎢ ⎥⎣ ⎦⎝ ⎠ ⎣ ⎝ ⎠⎦

(12)

{ }( )5

2

50 78 1 exp 37.5 ln100

10/

0.92 ln 5 ln10

sh

RHw

w v s

c

for c/p 0.65

ε −

− + − +

′ = ×

− −

≥

⎡ ⎛ ⎞ ⎤⎜ ⎟⎢ ⎥⎝ ⎠

⎢ ⎥⎢ ⎥⎛ ⎞ ⎡ ⎛ ⎞⎤

⎜ ⎟ ⎜ ⎟⎢ ⎥⎢ ⎥⎣ ⎦⎝ ⎠ ⎣ ⎝ ⎠⎦

(13)

For the high strength SCC with range of applicability (with range of applicability same as creep proposed model):

( ) ( ) ( )0 0 0, , ,cs ds ast t t t t tε ε ε′ ′ ′= + (14)

( ) ( )( )

00

0

, dsds

t tt t

t tε

εβ

∞′ −′ =

+ − (15)

( )6

0

10dsds t

ρεε

η−

∞

′′ = × (16)

( ) ( ) 1

,28

1 /1000.015 1.35 ( / )

4001 110 exp

ds

c d

RH wc p

f

for c/p<0.65

ρ

αε

−−′ = × +

+ −′

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎧ ⎫⎢ ⎥⎨ ⎬⎢ ⎥⎣ ⎩ ⎭ ⎦

(17)

( ) ( ) 1

,28

1 /1000.015 1.05 ( / )

4101 110 exp

ds

c d

RH wc p

f

for c/p 0.65

ρ

αε

−−′ = × +

+ −′

≥

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎧ ⎫⎢ ⎥⎨ ⎬⎢ ⎥⎣ ⎩ ⎭ ⎦

(18)

0

4 /100 0.7

w v st

β =+

(19)

( )( )[ ] 415 exp 0.007 28 0.25 10cf wη −′= + × (20)

( ) ( ) ( )0 0,as as ast t t tε ε ε′ ′ ′= − (21)

( ) ( ){ } 61 exp 10bas as st a t tε γ ε −

∞′ ′= − − − ×⎡ ⎤⎣ ⎦ (22)

( ){ }3070 exp 7.2 /as w cε ∞′ = − (23)

α = 11 for normal and low heat cement or α = 15 for high early strength cement. where, for t0, t' and t is re-placed by the temperature adjusted concrete age and γ is a coefficient representing the influence of the cement and admixtures type (maybe 1 when only ordinary Port-land cement is used). The variations of a and b constants with w/c ratio are given in Table 13.

6. Discussion of the proposed models

Proposed creep and shrinkage models are useable for lower and higher c/p and are adjusted to the normal and high strength SCC. In creep model non-linear creep amplification function (Eq. (3)) is added to the creep model that shown influential stress function on the creep behavior. The proposed creep model is adjusted to nor-mal and high strength SCC. Furthermore, SCC loading age parameter is included in the creep model as Eq. (5).

But, before to analyze the predictability of the pro-posed models it is important to inform that although shrinkage and creep are not totally independent phe-nomena (Neville, 1983; Bažant, 1994; Reinhardt, 2006), in this experimental program, the total strain was roughly understood as being composed by the addition of these independent phenomena. Consequently, ex-perimental results of creep strain used to verify the pre-dictability of the proposed creep model were determined as the difference between the total strain and shrinkage strain (Leemann, 2011, Reinhardt, 2006, CEB-FIB, 2010). Besides, according to the experimental data re-ported above, the following parameters were considered in the predictability of the proposed models: RH, w, c, w/c, v/s, c/p and f'cd,28d that are clear from the experi-mental program.

Figure 4 shows comparison of the proposed creep model with the available experimental results of creep. Analyzing the Fig. 4 one observes that the proposed

Table 13 Variations of a and b constants with w/c ratio.

w/c a b 0.20 1.2 0.4 0.23 1.5 0.4 0.30 0.6 0.5 0.40 0.1 0.7 ≥0.50 0.03 0.8


model provide an accurate prediction. In fact, most of the creep results predicted by the proposed model were slightly overestimated but always with a difference lower than 10% to the experimental results. As shown in the Fig. 4, the proposed creep model provided better prediction of creep data for SCC mixture with a coeffi-cient of correlation factor (R2) of 0.93, 0.95, 0.92 and 0.91 compared to N-SCC, D-SCC, S-SCC, and DS-SCC experimental results.

In terms of the proposed shrinkage model, Fig. 5 shows a comparison of the SCC shrinkage from experi-mental results versus calculated values from proposed model for (a) N-SCC, (b) D-SCC, (c) S-SCC, and (d) DS-SCC mixes. Observing Fig. 5, roughly speaking, one notes that the proposed model provided a good pre-diction. The predicted results were mostly conservative (especially after the age of 300 days), the maximum difference (10%) between predicted and experimental results. As shown in the Fig. 5, the proposed shrinkage model provided better prediction of creep data for SCC mixture with a coefficient of correlation factor (R2) of 0.91, 0.93, 0.90 and 0.89 compared to N-SCC, D-SCC, S-SCC, and DS-SCC experimental results.

7. Conclusions

The predictability of deformation models have been investigated for CC and SCC in this paper. Two new models are proposed for an accurate prediction of creep and shrinkage for concrete structures made with HSSCC. Based on comparisons between different models and on comparisons to the experimental results, the following conclusions can be drawn from this study: • For the CC mixtures the AASHTO (2007) and JSCE

(2002) models provided better predictions of the creep and shrinkage data compared to the other mod-els. Although the Eurocode 2 (2004) and AASHTO (2004) models had provided suitable predictions for creep they were not so successfully for shrinkage.

• For the SCC mixtures the JSCE (2002) model pro-vided better predictions of the creep and shrinkage data compared to the other models because of the certain intrinsic and/or extrinsic variables. The AASHTO (2004) and ACI 209R (1992) CC models provided also suitable predictions for creep and the AASHTO (2007) and AS 3600 (2009) CC models provided also suitable predictions for shrinkage.

(a) (b)

(c) (d)

Fig. 4 Comparison of the SCC creep from experimental results versus calculated values from proposed model for (a) N-SCC, (b) D-SCC, (c) S-SCC, and (d) DS-SCC mixes.


• The proposed creep and shrinkage models have good predictions high strength the SCC mixtures. The comparison between the predicted values and the ex-perimental results conducted in this study showed that the proposed models were able to predict creep and shrinkage with high accuracy.

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Notation w = water c = cement

/v s = volume to surface ratio /w c = water to cement ratio /c p = cement to powder ratio cf ′ = compressive strength

( )cmf t = mean value of compressive strength at time t ,28c df ′ = compressive strength at the age of 28 days

RH = relative humidity (%) 0 ,t t′ and t = effective age (days) of concrete at the be-

ginning of drying, at the beginning of loading, and during loading respectively

cpσ ′ = creep stress unit ,μ λ andα = parameters to be obtained from a least

square minimization procedure s′ and n = parameters that have to be specifically cali-

brated for each SCC concrete mix by using experimental results

κ = is a conventional scalar damage index shε ′ = final value of shrinkage strain

0( , )cs t tε ′ = shrinkage strain of concrete from age to t 0( , )ds t tε ′ = drying shrinkage strain of concrete from age

to t dspε ′ = the final value of drying shrinkage strain dsε ∞′ = final value of drying shrinkage

0( , )sc t tε ′ = shrinkage strain of concrete from age of 0t to t

0( , )as t tε ′ = autogenous shrinkage strain of concrete from the start of setting to age t

asε ∞′ = final value of autogenous shrinkage strain crε ′ = final value of creep strain per unit stress bcε ′ = final value of basic creep strain per unit

stress dcε ′ = final value of drying creep strain per unit

stress 0( , , )cc t t tε ′ ′ = creep strain

α = coefficient representing the influence of the cement type

β = represents time dependency of drying shrink-age

γ = coefficient representing the influence of the cement and admixtures type (γ may be 1 when only ordinary Portland cement is used)

η = constant related to compressive strength and water content

t = is the temperature adjusted concrete age, 0t = starting drying concrete age,

a and b = constants itΔ = the number of days where the temperature T

prevails ( )iT tΔ = the temperature (°C) during the time period

itΔ 0T = 1 °C

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